A moment matching method for option pricing under stochastic interest rates

TL;DR

This paper introduces a Gaussian moment matching approximation for pricing call options in markets with stochastic interest rates, demonstrating high accuracy and efficiency across various models.

Contribution

It presents a novel, general approximation method for option pricing under stochastic interest rates, applicable to affine and non-affine models, with validated performance against benchmarks.

Findings

High accuracy compared to Monte Carlo simulations

Efficient computational performance

Outperforms existing affine and expansion methods

Abstract

In this paper we present a simple, but new, approximation methodology for pricing a call option in a Black \& Scholes market characterized by stochastic interest rates. The method, based on a straightforward Gaussian moment matching technique applied to a conditional Black \& Scholes formula, is quite general and it applies to various models, whether affine or not. To check its accuracy and computational time, we implement it for the CIR interest rate model correlated with the underlying, using the Monte Carlo simulations as a benchmark. The method's performance turns out to be quite remarkable, even when compared with analogous results obtained by the affine approximation technique presented in Grzelak and Oosterlee (2011) and by the expansion formula introduced in Kim and Kunimoto (1999), as we show in the last section.